Question: $ C = \left[\begin{array}{rr}-2 & 2 \\ 0 & -2 \\ -2 & 3\end{array}\right]$ $ B = \left[\begin{array}{rrr}-1 & -1 & 2 \\ 2 & 3 & 1 \\ 4 & 2 & -1\end{array}\right]$ Is $ C B$ defined?
Explanation: In order for multiplication of two matrices to be defined, the two inner dimensions must be equal. If the two matrices have dimensions $( m \times  n)$ and $( p \times q)$ , then $ n$ (number of columns in the first matrix) must equal $ p$ (number of rows in the second matrix) for their product to be defined. How many columns does the first matrix, $ C$ , have? How many rows does the second matrix, $ B$ , have? Since $ C$ has a different number of columns (2) than $ B$ has rows (3), $ C B$ is not defined.